Sovran’s earnings jumped by 24 percent during the third quarter as the company’s Uncle Bob’s self-storage facilities ended the summer with occupancy levels that topped 90 percent for the second straight quarter.

And with demand on the upswing, Sovran was able to charge more to consumers looking to rent space. The company’s average rental rates rose by 3.6 percent.

Sovran’s earnings jumped to $31.1 million, or 98 cents per share, up from $25.1 million, or 85 cents per share, a year ago. The earnings topped analyst expectations by a penny.

And Sovran executives said they expect earnings to shoot up by about 29 percent during the current quarter to between 98 cents and $1 per share, compared with 77 cents per share a year ago. That’s slightly better than the 97 cents per share that analysts were expecting.

With plenty of customers looking to rent self-storage facilities, Sovran was able to raise its average rents to $11.07 per square foot at its stores that have been open for at least a year, up from $10.69 a year ago. Nearly 10 percent of Sovran’s customers were hit with a rate increase during the quarter, about double the percentage of a year ago, said Edward Killeen, a Sovran vice president.

“Pricing power continues to show in the rents we collected,” said Andrew J. Gregoire, Sovran’s chief financial officer.

That also allowed the company to reduce the value of the concessions it offers to many customers who are beginning to rent one of its self-storage units. Sovran operates 475 self-storage facilities in 25 states, mostly in the eastern half of the country. Sovran offered concessions to just 40 percent of its new customers during the summer, down from 48 percent in the spring and 56 percent a year ago. The value of those discounts has dropped by 45 percent, falling to $770,000 during the third quarter, compared with $1.2 million at the beginning of the year.

Even so, Sovran’s customers are sticking around longer, with 56 percent staying for more than a year, up from 54 percent a year ago.

“We’re trying to reduce the churn a little bit,” Rogers said.

Sovran said the company bought three additional stores during the quarter, including two on Long Island and one in Colorado, for a total purchase price of $27.9 million. The company also has deals to buy two other properties, one in Toms River, N.J., and the other in Palm Beach, Fla., for a combined price of $14.9 million.

The company also agreed to lease four stores on Long Island and western Connecticut and rebrand them under its Uncle Bob’s name. The company sold its only store in Dayton, Ohio, for $3.2 million.

The company’s shares closed down $2.20, or 2.94 percent, at $72.60 Wednesday.